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fixed circumradius, 2 circles All-Russian MO 1995 Regional (R4) 9.3

Source:

August 26, 2024

geometrycircumcircle

Problem Statement

Two circles with radii

R

and

r

intersect at

C

and

D

and are tangent to a line

\ell

A

and

B

. Prove that the circumradius of triangle

ABC

does not depend on the length of segment

AB